Taiwanese Journal of Mathematics

Maximal Regularity for Integral Equations in Banach Spaces

Shangquan Bu

Full-text: Open access

Abstract

We study maximal regularity in periodic Besov spaces $B_{p,q}^s(\mathbb T, X)$ for the integral equations ($P$): $u(t) = A \int^{t}_{-\infty} a(t-s) u(s) ds) + B \int^{t}_{-\infty} b(t-s) u(s) ds + f(t)$ on $[0,2\pi]$ with periodic boundary condition $u(0) = u(2\pi)$, where $A$ and $B$ are closed operators in a Banach space $X$, $a, \ b \in L^1(\mathbb R_+)$ and $f$ is a given function defined on $[0,2\pi]$ with values in $X$. Under suitable assumptions on the kernels $a, \ b$ and the closed operators $A, \ B$, we completely characterize $B_{p,q}^s$-maximal regularity of ($P$).

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 229-240.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406172

Digital Object Identifier
doi:10.11650/twjm/1500406172

Mathematical Reviews number (MathSciNet)
MR2780282

Zentralblatt MATH identifier
1245.45009

Subjects
Primary: 45N05: Abstract integral equations, integral equations in abstract spaces
Secondary: 45D05: Volterra integral equations [See also 34A12] 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 47D99: None of the above, but in this section

Keywords
Fourier multiplier maximal regularity integral equation Besov spaces

Citation

Bu, Shangquan. Maximal Regularity for Integral Equations in Banach Spaces. Taiwanese J. Math. 15 (2011), no. 1, 229--240. doi:10.11650/twjm/1500406172. https://projecteuclid.org/euclid.twjm/1500406172


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